Known in the prior art is the one-piece flanged, hinged container package of plastic, which is made by thermoforming and die-cut trimming, into an open container of two complementary package portions, usually halves, that are connected by a hinge portion, whereby either of the two package portions may swing about the hinge portion to form a closed container or package. The roof of the hinge, through the entire length of the hinge, is above and parallel to the flange plane, supported by the sidewalls of the hinge, which sidewalls have an undercut slant, i.e. are not perpendicular to the flange but are slanted therefrom with a negative draft along their entire length, from end-to-end. When the die-cut trimming occurs, the cutting through the raised roof of the hinge causes deformation of the hinge. This deformation may not necessarily hinder the function of the hinge, but sometimes it does, and at the least, it degrades the aesthetics of the package. Further, however, this crush-cutting causes the sidewalls of the hinge to collapse as the cut is made, the cut being completed as the sidewalls are in the collapsed state with part of the hinge plastic folded over itself. This results in a sharp burr, spear or spike of plastic protruding from each end corner of the hinge. In using the package, these sharp protrusions can cut through a person's skin, and can also pierce through outer packaging materials that cover the thermoform package. In medical packaging, such outer covers are often used to seal in a sterilized thermoform package, and this piercing can destroy the sterility that has been provided.